uwloo

PMATH 451Measure and Integration

Units
0.50
Faculty
Mathematics
Subject
Pure Mathematics

Not in the current Undergraduate Calendar. Shown as it appeared in 2024–25.

When it runs

  1. F24
  2. W25
  3. S25
  4. F25
  5. W26
  6. S26
  7. F26
  8. W27
  9. S27

Ran in 2 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.

General measures, measurability, Caratheodory Extension theorem and construction of measures, integration theory, convergence theorems, Lp-spaces, absolute continuity, differentiation of monotone functions, Radon-Nikodym theorem, product measures, Fubini's theorem, signed measures, Urysohn's lemma, Riesz Representation theorems for classical Banach spaces.

Prerequisites

  • Earned a minimum grade of 60% in each of the following:
    • PMATH450 - Lebesgue Integration and Fourier Analysis (0.50)

Antirequisites

None listed.

Leads to

No course lists it as a requisite.

Reviewed on UW Flow

83% liked it75% easy100% useful

From 6 ratings and 3 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • Had it with Matthew Kennedy (Fall 2024). Hard assignments but doable within time constraints. Wasn't at all well prepared for the final exam type of question, for which 50% of the question style is different from the practice final provided or the assignments throughout the course.

    Dec 2024 · didn’t like itOn UW FlowRemove this

  • The concepts are not overly difficult, although the assignments - despite providing a lot of insight - can be long and slightly bashy at times. Someone who has already taken PMATH 450 would find this course helpful in cementing their knowledge, but this course is also accessible - if not slightly challenging - to people without that background. The material taught was surprisingly useful outside of the course. It's been probably my favourite 400-level math class so far, definitely would recommend.

    Jan 2024 · liked itOn UW FlowRemove this

  • Pretty straightforward and easy course. Materials are nearly identical to PMATH 450 so make sure to review those and you'll be fine.

    Apr 2023 · liked itOn UW FlowRemove this

Discussed on r/uwaterloo

101 posts and comments in 90 threads mention PMATH 451, May 2012 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.

Fall 2024

Winter 2024

Interesting pmath/co courses? 3 points, 2 comments

“What are some particularly interesting pmath/co courses? I don’t have space to take many of them, but wish to maximize my utility. One course I know I want to take is pmath 351. Any other suggestions?”

u/Alone_Letterhead2671: “… PMATH Analysis route: PMATH 450, 451, 453 which are pretty popular. Some topics covered are pretty cool like Measure theory covered in more rigorous version. It's also applicable in lots topic like probability theory, analytics NT, operator theory, optimization, etc. …”

u/Stranger_Natural: “Seconding this, but I also wanted to mention that measure theory (pmath 450, 451) and functional analysis (453) gets used in certain pmath (analysis), co (optimization), and stats (stochastic calculus) topics courses (which you can try to take as an undergrad). …”

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How much work is STAT 241? 6 points, 3 comments

u/Stranger_Natural: “… Thinking about taking it, I'd say I have decent math background (I've taken a couple of PMATH and CO), and I have some knowledge of measure theory (taking PMATH 451 rn, I vaguely remember), but I'm a bit rusty on my STAT 230. …”

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Fall 2023

Taking only the analysis PMATH courses 3 points, 6 comments

“Is it possible to be successful in taking only the analysis related PMATH courses? How related are the other ones (group theory, geometry)? I also only took regular math235 and not the advanced one.”

u/weil_conjecture: “What does \successful' mean (in this context)?”

u/Bid_Queasy: “Yeah, you just need smt equivalent to PMATH 451 and that should be more than enough for most stats related stuff.”

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Spring 2023

Is it possible to get the schedule changed? 1 point, 6 comments

u/Important-Koala-1516: “The schedule for the Fall term was out, but I noticed that two of my selected courses have time conflict, in particular, PMATH347 and PMATH451 are both 8:30-9:20am MWF. I was wondering if it is possible to petition for a change in schedule.”

u/ClarkeVice: “Sometimes it’s possible, but in this case it seems pretty unlikely. Unfortunately, some conflicts have to exist. Given PMATH 451 is an elective, it likely isn’t a priority to avoid a conflict with other courses.”

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Fall 2022

STAT 902 Undergraduate? 1 point, 11 comments

u/Novel_Brain9700: “Has anyone ever taken STAT 902 as an undergraduate before? What do the instructor usually ask as a prerequisite for the course? Do you actually need to take STAT 901 first (I heard that you need PMATH 451 for this)”

u/vkoj1221: “I havent taken STAT 901 or STAT 902 but I was allowed to take STAT 901 (as an undergrad with PMATH 450 but no STAT 330). I dropped out of the class because it was looking a little bit like PMATH 451 but easier. I imagine that overriding in is instructor dependent.”

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Fall 2021

Math double major??? 3 points, 13 comments

“I was wondering if it is possible for math students to double major in their second year when they declare their majors. …”

u/Fatdayuu: “That’s possible, I declared 3 majors last year and one of my friend declared 4. The course load is ok :)”

u/Fatdayuu: “Pmath are hard. I have 6 courses in this term, Pmath 451 453 930 and Actsc 372, Stat 331, CS246. I spent 70% of my time in Pmath :(”

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Check it elsewhere for Fall 2026

Calendar versions

Undergraduate Calendar